On the original question, 'to the nearest minute' seems to answer most of the question. At 29 seconds past the nearest minute is the one just past, at 31 seconds past the nearest minute is thew one just coming. No idea what happens at 30 seconds past though - perhaps its a bit like 2400, not used to avoid confusion.
Come to think of it,Bern who cares! And why did I bother sitting here and tring to offer my two pennyworth?
And another thing. Mr_Grubby, even though I've reached the age where I can come up with comments about CATC and the like that will date me, when your clock showed 12345678, I was still at school.
Ahh, that feels better!